### Abstract

In Green’s function diakoptics, wavefield interactions between disjoint domains in space
are described in terms of interacting multi-port subsystems
In addition to integral-equation based Green’s function diakoptics for time-harmonic fields,
a demonstrably stable discrete space-time Green’s function diakoptics scheme has been reported to be effective for proximate regions. For distant regions it is necessary to retain a long field history. Upon considering a diakoptics toy problem involving two disjoint domains consisting of a single point each, the resulting boundary operator may be expressed
in terms of two distinct discrete Green’s functions only, describing the intra- and inter-domain unitsource field responses, respectively. There are various integral representations and asymptotic expansions for the discrete Z-domain Green’s functions, and it is even possible to construct representations for the discrete space-time Green’s functions consisting of nested finite sums, which turn out to be difficult to evaluate due to severe
cancellations.

Original language | English |
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Title of host publication | Proceedings of the 2010 International Conference on Electromagnetics in Advanced Applications (ICEAA '10), September 20-24, 2010, Sydney, Australia |

Place of Publication | Piscataway |

Publisher | Institute of Electrical and Electronics Engineers |

Pages | 565-568 |

ISBN (Print) | 978-1-4244-7367-0 |

Publication status | Published - 2010 |

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## Cite this

Hon, de, B. P., & Arnold, J. M. (2010). Discrete Green's function diakoptics : a toy problem. In

*Proceedings of the 2010 International Conference on Electromagnetics in Advanced Applications (ICEAA '10), September 20-24, 2010, Sydney, Australia*(pp. 565-568). Institute of Electrical and Electronics Engineers.